Analysis of Computer Experiments with Functional Response

TL;DR

This paper develops a Gibbs sampling-based EM algorithm to transform irregular functional data into a regular grid, enabling efficient kriging modeling of complex residual stress profiles in metal machining.

Contribution

It introduces a novel EM algorithm that handles irregularly spaced functional data, facilitating kriging analysis in high-dimensional computer experiments.

Findings

Efficiently converts irregular data to regular grid for kriging.

Enables application of Kronecker product techniques to complex functional data.

Improves modeling of residual stresses in metal machining.

Abstract

This paper is motivated by a computer experiment conducted for optimizing residual stresses in the machining of metals. Although kriging is widely used in the analysis of computer experiments, it cannot be easily applied to model the residual stresses because they are obtained as a profile. The high dimensionality caused by this functional response introduces severe computational challenges in kriging. It is well known that if the functional data are observed on a regular grid, the computations can be simplified using an application of Kronecker products. However, the case of irregular grid is quite complex. In this paper, we develop a Gibbs sampling-based expectation maximization algorithm, which converts the irregularly spaced data into a regular grid so that the Kronecker product-based approach can be employed for efficiently fitting a kriging model to the functional data.